Theoretical model to analyze the non-repetitive run-out (NRRO) of ball bearings

The constant increase in the requirement of running precision is leading to the fact that the operation reliability constraints are increasingly compelling designers to make an in-depth understanding of the constitutive relationship between the geometrical errors and the non-repetitive run-out (NRRO) of an angular contact ball bearing under low-speed running case. A methodology that enables a theoretical analysis approach to clarify this special constitutive relationship is presented in this paper. First, we develop a numerical model of NRRO based on the relationship of the internal movement and their dimensional chain, which the effects that load have on the contact angle, is taken into consideration. In this model, the geometrical errors of rings raceway and balls are modeled by the superposition of sinusoidal function, the Hertzian contact theory is used to calculate the contact angle and build the equations to solve the internal dimensional chain of ball bearings; Then, we calculated the trajectory of rotation center by solving the nonlinear equations of internal balance force to quantitative analysis the NRRO of a ball bearing caused by the geometrical errors of rings raceway and balls, the diameter differences of balls and their distribution; Finally, the methodology developed has been applied to a real application for SKF 7218 bearing, and the results indicate that the number of balls is the optimum design.